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Coq Modulo Theory

by Pierre-yves Strub , 2010
"... Abstract. Coq Modulo Theory (CoqMT) is an extension of the Coq proof assistant incorporating, in its computational mechanism, validity entailment for user-defined first-order equational theories. Such a mechanism strictly enriches the system (more terms are typable), eases the use of dependent types ..."
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Abstract. Coq Modulo Theory (CoqMT) is an extension of the Coq proof assistant incorporating, in its computational mechanism, validity entailment for user-defined first-order equational theories. Such a mechanism strictly enriches the system (more terms are typable), eases the use of dependent

ELAN for Equational Reasoning in Coq

by Cuihtlauac Alvarado, Quang-Huy Nguyen, Loria Inria Lorraine , 2000
"... We describe an interface between Coq, an interactive theorem-prover based on type theory and ELAN, an automated deduction system based on rewriting logic. Our objective is to provide efficient tools to implement decision procedures using equational reasoning in Coq. ELAN is used as a rewrite engine. ..."
Abstract - Cited by 12 (3 self) - Add to MetaCart
We describe an interface between Coq, an interactive theorem-prover based on type theory and ELAN, an automated deduction system based on rewriting logic. Our objective is to provide efficient tools to implement decision procedures using equational reasoning in Coq. ELAN is used as a rewrite engine

A formalization of Γ ∞ in Coq

by Robbert Krebbers , 2010
"... In this paper we present a formalization of the type systems Γ ∞ in the proof assistant Coq. The family of type systems Γ∞, described in a recent article by Geuvers, McKinna and Wiedijk [9], presents type theory without the need for explicit contexts. A typing judgment in Γ ∞ is of the shape A: ∞ B ..."
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In this paper we present a formalization of the type systems Γ ∞ in the proof assistant Coq. The family of type systems Γ∞, described in a recent article by Geuvers, McKinna and Wiedijk [9], presents type theory without the need for explicit contexts. A typing judgment in Γ ∞ is of the shape A: ∞ B

An approach to Real Numbers in Coq

by Alberto Ciaffaglione, Pietro Di Gianantonio
"... Introduction The aim of this work is to propose and discuss a representation of Real Numbers in the context of Logical Frameworks, i.e. generic interactive proof assistants based on Type Theory. This is a first step towards computer assisted reasoning on reals, and it should provide a workbench for ..."
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Introduction The aim of this work is to propose and discuss a representation of Real Numbers in the context of Logical Frameworks, i.e. generic interactive proof assistants based on Type Theory. This is a first step towards computer assisted reasoning on reals, and it should provide a workbench

BAGAHK: DEVELOPING SOUND AND COMPLETE DECISION PROCEDURES IN COQ

by Benjamin J. Delaware , 2007
"... Decision procedures are automated theorem proving algorithms which automatically recognize the theorems of some decidable theory. The correctness of these algorithms is important, since a design error could lead to the misidentification of a false statement as a theorem. In the past, decision proced ..."
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decision procedure for a theory T is correct, it must also be shown to be complete in that it recognize all true propositions from T. We have developed a decision procedure called bagahk for the validity of formulas modulo the theory of ground equations T=, which we have proven sound and complete

Essential Incompleteness of Arithmetic Verified by Coq

by unknown authors , 2006
"... Abstract. A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive fu ..."
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Abstract. A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive

Essential Incompleteness of Arithmetic Verified by Coq

by unknown authors , 2005
"... Abstract. A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive fu ..."
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Abstract. A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive

Encoding Kleene Algebra (with tests) in Coq ⋆

by Nelma Moreira, David Pereira, Simão Melo De Sousa
"... Kleene algebra [1], (KA) normally called the algebra of regular events, is an algebraic system that axiomatically captures properties of several important structures arising in Computer Science, and has been applied in several contexts like automata and formal languages, semantics and logic of progr ..."
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. In order to provide a proof that regular languages are a model of KA, we have encoded regular languages, by extending Coq's Ensembles library of basic set theory with new inductive types for the concatenation and Kleene's star operations, based in the work of J.C. Filliâtre [6]. In what concerns

Author manuscript, published in "Logic In Computer Science (LICS 2010) (2010)" Coq Modulo Theory

by Pierre-yves Strub, Qian Wang , 2010
"... Theorem provers like COQ [3] based on the Curry-Howard isomorphism enjoy a mechanism which incorporates computations within deductions. This allows replacing the proof of a proposition by the proof of an equivalent proposition obtained from the former thanks to possibly complex computations. Adding ..."
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more power to this mechanism leads to a calculus which is more expressive (more terms are typable), which provides more automation (more deduction steps are hidden in computations) and, most importantly, eases the use of dependent data types in proof development. COQ was initially based on the Calculus

A constructive denotational semantics for Kahn networks in Coq

by Christine Paulin-mohring, Inria Futurs , 2007
"... Semantics of programming languages and interactive environments for the development of proofs and programs are two important aspects of Gilles Kahn’s scientific contributions. In his paper “The semantics of a simple language for parallel programming ” [11], he proposed an interpretation of (determin ..."
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of (deterministic) parallel programs (now called Kahn networks) as stream transformers based on the theory of complete partial orders (cpos). A restriction of this language to synchronous programs is the basis of the data-flow Lustre language which is used for the development of critical embedded systems [14, 10
Results 1 - 10 of 120